Introduction

Globally, wetlands are net sinks for atmospheric carbon dioxide (CO2) but can be large sources of methane (CH4), thus playing a critical role in regulating global warming (Mitsch et al. 2013). Currently, a total of 181 Tg of CH4 is emitted from global wetlands each year, accounting for 28% of the global CH4 emissions despite wetlands only making up 5–8% of the world’s land surface area (Saunois et al. 2020). Because of the much stronger global warming effect made by CH4 relative to an equivalent emission of carbon as CO2, the emissions of CH4 can reduce the net climate impact of wetland carbon sinks (Liu et al. 2020; Rosentreter et al. 2023) or even cause wetlands to have a net warming impact on radiative forcing (Mitsch et al. 2013; Yuan et al. 2021). To improve model predictions of how carbon balances and net radiative forcing effects of wetland ecosystems will respond to future climate change scenarios, improved model representations of subsurface biogeochemical CH4 cycling that control CH4 emissions are necessary (Bridgham et al. 2013). CH4 emissions are regulated by methanogenesis and methane oxidation rates, plant traits related to gas transport and depending on soil redox conditions, O2 availability, and availability of alternative electron acceptors, e.g., sulfate and iron, in wetlands soil porewater.

Wetland plants can transport oxygen from the atmosphere through tissue channels called aerenchyma lacunae into rhizomes and roots, which can then release oxygen into the immediate external soil porewater, a process termed radial oxygen loss (ROL) (Armstrong 1972; Justin and Armstrong 1987). This is a strategy of wetland plants to overcome hypoxia by supporting respiration and creating oxidative protection from phytotoxins such as sulfide (Lamers et al. 2013; Martin and Maricle 2015) in waterlogged conditions. The oxygen delivered into soil porewater by ROL can increase O2 availability and facilitate aerobic decomposition and methane oxidation. It can also facilitate anaerobic decomposition by re-oxidizing reduced species into alternative electron acceptors (e.g., Fe3+, SO42−) (Sundby et al. 2003; Wolf et al. 2007; Fritz et al. 2011; Mueller et al. 2016). Specifically, in coastal wetlands, sulfur cycling (sulfate reduction and sulfide oxidation) can influence methane fluxes by competing for organic carbon substrate and O2. Sulfur cycling might have larger impacts with increasing salinization driven by sea-level rise, which can bring in more sulfate to the coastal wetlands. Previous studies implied that ROL can affect how wetlands greenhouse gases fluxes respond to global change. Mesocosms showed that in wetland ecosystems under elevated atmospheric CO2, soil carbon accumulation and methane emissions both decreased (Noyce et al. 2023) and CO2 emissions increased (Wolf et al. 2007). These changes in flux rates were likely caused by stimulated plant growth, including the more root development, and thus the increased ROL fluxes, which then enhanced aerobic decomposition and methane oxidation while inhibiting methanogenesis.

Besides increasing O2 availability, the O2 input from roots results in steep gradients of porewater O2 away from roots, thus causing spatial heterogeneity in porewater chemistry at the rooting zone (Armstrong et al. 2000; Sundby et al. 2003; Bezbaruah and Zhang 2005). This spatial heterogeneity of O2 distribution at the root scale determines the heterogeneous microbial reaction rates and heterogeneous distribution of redox sensitive chemical species, which ultimately impact the CH4 flux on larger scales (Segers et al. 2001). One of the challenges in simulating CH4 fluxes in vegetated wetlands lies in the need to scale from microbial scales, where dynamics are non-linear and process parameters may be highly uncertain, to larger scales, where model complexity must be reduced for computational reasons (Segers and Leffelaar 2001a). Ideally, these challenges can be addressed by developing step-wise scaling and simplification schemes to avoid biases in predicted porewater constituents and fluxes (Segers and Leffelaar 2001b, Segers et al. 2001). On the smallest scale, microbial reaction rates are typically nonlinear functions of the substrate concentrations. To scale from here to the next scale (e.g. a soil layer), predictions of microbial rates based on the mean of the substrate will be distinct from predictions based on taking the mean of the function’s evaluations at each value of the substrate (Sierra et al. 2011, demonstration in Fig. S1). Bias in the calculated porewater CH4 concentration can further cause bias in the integrated CH4 fluxes over larger scales (Segers and Leffelaar 2001a, b; Segers et al. 2001).

Currently, the ROL process is underrepresented in wetland biogeochemical models (O’Meara et al. 2021), despite some early developments in ROL simulations for peatlands (Arah and Stephen 1998; Segers and Leffelaar 2001a, b; Segers et al. 2001). Due to computational demands and lack of information of subsurface heterogeneity, Earth system models do not resolve fine-scale horizontal O2 heterogeneity (Riley et al. 2011; Golaz et al. 2019). Typically, Earth system models distinguish aerobic and anaerobic zones in a soil profile based on water table, calculate mean gas porewater concentrations for different homogeneous soil layers, and estimate greenhouse gas fluxes (Wania et al. 2013; Golaz et al. 2019; Shu et al. 2020). Current models therefore assume anoxic conditions for inundated wetland soil and horizontal homogeneity, but field observations have shown that ROL can supply a substantial amount of oxygen into fully water-saturated soil and cause horizontal heterogeneity of O2 distribution at the rooting zone (e.g., Sundby et al. 2003).

There has not been quantitative assessment of the importance of ROL and its spatial heterogeneity to the modeling of porewater biogeochemistry and methane fluxes, so it is unclear whether and how such heterogeneity should be incorporated into Earth system models. In this study, we developed ROL simulation in a numerical model for coastal wetland biogeochemistry to quantify the impacts of the ROL and spatial heterogeneity on model predictions of porewater concentrations and CH4 emissions. We hypothesized that (1) addition of simulated ROL will reduce porewater concentration of CH4 at the root tips with O2 input and reduce CH4 flux and (2) simulated heterogeneous ROL will decrease CH4 and H2S concentrations and CH4 emissions compared to homogeneous ROL simulation because oxidation rates locally (at the root scale) are higher in the heterogeneous scenario. We used the reactive transport model, PFLOTRAN (Hammond et al. 2014), for our simulations. We first created a three-dimensional soil profile as our simulation domain to resolve the fine-scale spatial heterogeneity caused by ROL. We then defined a reaction network representing the key subsurface biogeochemical processes in coastal wetlands. Meanwhile, we developed approaches to simulate CH4 emissions and ROL O2 injection within the PFLOTRAN framework, as PFLOTRAN does not have internal functions to simulate plant-mediated transport or bubbling of gas species (Wang et al. 2024). Three modes of ROL were tested, i.e., no ROL, homogeneous ROL, and heterogeneous ROL. We coupled the reaction network with each of these three ROL modes to model the soil porewater concentrations of redox sensitive species and CH4 fluxes at steady state. We analyzed the differences in model output between the three ROL modes to quantify the effects of incorporating ROL and the associated spatial heterogeneity on model predictions of porewater concentrations and CH4 fluxes.

Methods

Simulation domain

To assess the impact of homogeneous and heterogeneous ROL, we developed new simulations using the chemical reaction solver PFLOTRAN (Hammond et al. 2014). PFLOTRAN has been used successfully to represent the complex redox reaction network in coastal wetlands soil models (O’Meara et al. 2024; Wang et al. 2024), and it has shown promise to be coupled to large-scale land surface models (Tang et al. 2016). It is a powerful tool to simulate complex chemical processes but does not itself contain ecological processes such as vegetation growth and litter deposition (O’Meara et al. 2024). However, vegetation function and other ecological boundary conditions can be supplied via coupling to land surface models (Tang et al. 2016). Here, we use PFLOTRAN to represent ROL as injection of oxygen into anoxic soil and assess the impact on porewater constituents. Representing plant functions is beyond the scope of this study.

We set up a simulation domain of \(10\, \text{c}\text{m}\times 10\, \text{c}\text{m}\times 70\, \text{c}\text{m}\) with a porosity of 0.8 (Fig. 1). The porosity value was taken from measurements at tidal marshes at the Delaware River Estuary (Weston et al. 2014). The simulation domain was divided up into 9 layers, with the thickness of each layer increasing with depth, and then each layer was divided into \(10\times 10\) horizontal grids evenly, for a total of 900 calculation cells in the domain (Fig. 1). We set up the dimensions and discretization of this simulation domain to represent a patch of soil that is sufficient to accommodate 15 roots for creating belowground spatial heterogeneity, resolve the dimension of individual roots (diameter 1–2 mm), and represent the thickness of soil organic carbon-rich layer (40–100 cm deep) of tidal marshes.

In this study, model parameterization relevant to root distribution and ROL was based on measured data or observations for Typha angustifolia, which dominates the vegetation in many tidal marshes in North America (Snyder 1993). The horizontal spatial resolution of the domain was 1 cm, greater than the diameter of the oxygen-releasing roots (1–2 mm) but smaller than the spacing between the roots (> 15 mm). Our model only injects O2 at depths of 7.5–15 cm, because the oxygen-releasing root tips typically reside at depths between 7.5 and 15 cm (see field example in Fig. S2). In our model setting, the pore space remained fully water-saturated during the simulation. Pore spaces were assumed to be fully water-filled, with no gas-filled pore space.

Fig. 1
figure 1

Discretization of the simulation domain. The simulation domain (10 cm × 10 cm × 70 cm) was divided into 10 × 10 × 9 cells. The domain was discretized along both the X and Y axes equally but more densely discretized closer to the top surface along the Z axis (the vertical axis representing soil column depth). The top surface of the simulation domain represents the sediment-air interface, parameterized by a boundary condition.

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The surface of the domain represents the sediment-air interface, which was defined as the upper boundary condition to keep the dissolved gas species in equilibrium with the atmosphere. The boundary condition and initial condition of the porewater concentrations are the same for the three ROL scenarios, summarized in Table 1.

PFLOTRAN calculated the changes in concentrations of chemical species in each cell based on the biogeochemical reaction network we defined for this study (Sect. Reaction network) and the transport of solute between cells based on diffusion laws. The diffusion coefficient was taken from Furukawa et al. (2004) and corrected for tortuosity following Boudreau (1996a).

Table 1 Boundary and initial conditions of chemical species concentrations. All three ROL modes used the same boundary condition and initial condition. All cells of the simulation domain were initialized with the initial condition
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Reaction network

We defined a biogeochemical reaction network incorporating key subsurface microbial reactions for coastal wetlands and parameterized reactions based on observation data and modeling studies. Because PFLOTRAN is primarily used for aqueous chemistry, to create a C source for our simulations, solid organic matter (SOM) was transformed via hydrolysis into DOM to incorporate in redox reactions. We assume a constant rate of hydrolysis at the time scale of our simulations. The aqueous reaction network consists of aerobic decomposition, methanogenesis, sulfate reduction, and aerobic oxidation of CH4 and H2S (Fig. 2; Table 2). In reaction stoichiometries, SOM and DOC were assumed to have the stoichiometry CH2O. Iron and Manganese cycling were not included in our simplified reaction network due to low concentrations and limited impact on methanogenesis in organic wetland soil (Weston et al. 2014; O’Meara et al. 2024; Määttä and Malhotra 2024).

Fig. 2
figure 2

Microbial reaction network defined in our model. Circles show chemical pools and lines show reactions. Microbial reactions: ① SOM hydrolysis, ② aerobic decomposition, ③ methanogenesis,④ CH4 aerobic oxidation, ⑤ sulfate reduction, H2S aerobic oxidation

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Reactions proceed at rates determined by substrate concentrations following the Monod function (Section S1.1). The Monod function parameters, i.e., rate constants (\({\nu }_{max}\)) and Monod half-saturation constants (K) of each substrate for each reaction (summarized in Table 2) were derived from observational data or taken from parameterization in modeling studies for wetland ecosystems (Section S1.2). We parameterized the reaction network as in Table 2 and performed simulations using those base parameterizations as the “standard model runs”. Subsequently, the values of \({\nu }_{max}\) and \({K}_{{O}_{2}}\) of aerobic oxidation were also varied to test the effects of ROL heterogeneity under different reaction parameterizations in a sensitivity analysis (Sect. Sensitivity analysis).

Table 2 Reaction stoichiometry, rate constants (\({\nu }_{max}\)), Monod half-saturation constants (K), and Monod half-saturation inhibition constants (K′) of each substrate for each reaction used in the standard model runs
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Different modes of ROL simulation

We designed three modes of ROL to be coupled with the reaction network: (1) no ROL (noROL), (2) homogeneous ROL (ROL_Hom), and (3) heterogeneous ROL (ROL_Het) (Fig. 3) and parameterized ROL simulations based on observation data. We used an O2 injection rate of 72 mmol m−2 (sediment surface) d−1 for the standard model runs (see section S1.3 for the derivation). Because our simulation domain had a sediment surface area of 0.01 m2, the total O2 injection rate for the entire simulation domain was 0.72 mmol d−1.

Fig. 3
figure 3

Conceptual diagram of the three modes of ROL. On the left are the three-dimensional views of the entire simulation domain. On the right are the views from top of the rooting zone layer showing the locations of the O2 injection spots and specifying the O2 injection rate into each grid cell. a1, a2 noROL. b1, b2 ROL_Hom, in which the O2 was injected equally to all 100 cells of the rooting zone. c1, c2 ROL_Het, in which the O2 was injected into 15 cells of the rooting zone. The total O2 injection rate into the entire simulation domain was the same for the ROL_Hom and ROL_Het modes (0.72 mmol d−1), which was divided by the number of O2 injection cells for each ROL mode

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For the noROL mode, no O2 was injected. For the ROL_Hom mode, O2 was injected equally into each cell of the rooting zone (7.5–15 cm deep), so the O2 injection rate for each cell was 0.0072 mmol cell−1 day−1. For the ROL_Het mode, O2 was injected into 15 root-representing cells of the rooting zone layer, so the injection rate into each root cell was 0.048 mmol cell−1 day−1. The location of the 15 root cells were assigned randomly, while excluding the outermost grid cells. Therefore, ROL_Hom and ROL_Het had the same total amount of O2 injected into the entire simulation domain, but the pattern of O2 injection was different between the two modes. In all three modes, our estimation of CH4 fluxes (Sect. Simulation and calculation of CH4 fluxes) was identical, so that we tested only differences in the ROL parametrization. All simulations had the same initial CH4 concentrations, which changed during simulation due to the microbial reactions (Sect. Reaction network) and gas transport (Sect. Simulation and calculation of CH4 fluxes).

Simulation and calculation of CH4 fluxes

Total surface CH4 flux consists of three components: (1) surface diffusion across the sediment-air interface, (2) plant-mediated transport through rhizome and aerenchyma out of the rooting zone, and (3) ebullition. The surface diffusive flux was directly provided by the PFLOTRAN output from its mass balance calculations of exchanges across the domain boundary. However, PFLOTRAN does not currently have internal representations of plant-mediated CH4 transport or ebullition. Therefore, we included two additional reaction network terms to represent CH4 removal from the subsurface and direct transport to the atmosphere and to keep track of the fluxes. We parameterized the reaction terms based on observation data of CH4 flux measurements (Supporting Information S1.4, Table S1). Effectively, during both plant-mediated transport and ebullition excess CH4 is instantaneously removed from the grid cells where either a root is located (for plant-mediated transport) or the ebullition threshold in CH4 concentrations (1.4 mM) is reached (for ebullition). The parametrization of methane transport across ROL simulations was kept identical, but it was activated in different cells across simulations. For ROL_Het, plant-mediated transport of CH4 proceeded only in the 15 rooting cells, i.e., same as the heterogeneous O2 injection. For ROL_Hom, plant-mediated transport of CH4 proceeded in all cells of the rooting zone. In the noROL mode, we kept plant-mediated transport of CH4 occurring in all cells of the rooting zone, so that only the ROL parametrization varies across simulations.

Model simulation and model output comparisons between different ROL modes

We performed simulations for the three ROL modes at timesteps of 1 min to 1 h (as determined by PFLOTRAN’s variable time stepping algorithm) for 10 days, at which time the porewater concentrations had reached a quasi-steady state. Provided the discretization of the simulation domain (100 sub-columns), the model output from each ROL mode simulation was 100 concentration profiles for each chemical species. We averaged the porewater concentrations over each layer of the domain to obtain the mean concentration profiles for each ROL simulation type. We calculated the percentage differences in the mean concentrations and the domain-integrated total CH4 flux between different ROL simulations (Eq. S2) to determine how explicitly accounting for fine-scale heterogeneity changed the outcome at larger scales.

Sensitivity analysis

We performed a sensitivity analysis to determine the impact of changing three drivers impacting ROL directly, \({K}_{{O}_{2}}\), total O2 injection rate, and number of grid cells with roots on the model result. We varied each of these three input variables separately, ran simulations under both the ROL_Hom and ROL_Het modes and then investigated how each input variable affected the percentage differences in the model output, i.e., domain-averaged porewater concentrations and domain-integrated CH4 flux. In addition, we ran the model without sulfur cycling (i.e. without sulfate reduction and sulfide oxidation) since sulfide oxidation can scavenge O2 from the soil. When the Monod half-saturation concentration of O2, \({K}_{{O}_{2}}\), was varied, the \({\nu }_{max}\) of the respective reaction was also varied following the relationship between \({\nu }_{max}\) and \({K}_{{O}_{2}}\) proposed by Vallino (2011). When the number of root cells was varied, the \({\nu }_{max}\) of the reaction term simulating plant-mediated transport was also varied to account for the changes in the number of root cells. The different parameters tested can be found in Table 3. To isolate the impact of each variable, only one parameter was varied at a time.

Table 3 The values of input variables tested in the sensitivity analysis. Note that simulations 1.1, 2.1, and 3.1 are indeed the same (that is the standard model run) but were displayed in the table repeatedly for clarification
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Results

Spatial distribution and concentrations of porewater constituents at the rooting zone

Simulated ROL increased O2 availability at the rooting zone. The noROL simulation had zero O2 (Fig. 4a). In the homogeneous ROL simulation (ROL_Hom), the injected O2 was nearly all consumed, resulting in a low O2 concentration of 0.01% saturation (Fig. 4b). In the heterogeneous ROL simulation (ROL_Het), the resulting O2 accumulated in the root cells (i.e., the O2 injection spots), reaching 1–100% saturation, and 0% saturation in the non-root cells (Fig. 4c). O2 accumulation was more pronounced at the region with more O2 injection cells, i.e., the top left corner of the rooting zone (Fig. 4c).

Fig. 4
figure 4

Spatial distribution and concentration ranges of porewater constituents at the rooting zone layer predicted from different ROL simulation modes: a1–a5 noROL, b1–b5 ROL_Hom, c1–c5 ROL_Het. The O2 availability increased by 1–2% with ROL. The ROL_Hom had very little impact on O2, CH4, and DOC concentrations but it predicted much higher SO42− and lower H2S concentrations when compared to noROL. The ROL_Het resulted in heterogeneous distribution of redox sensitive constituents: O2 and SO42− were higher and CH4, DOC, and H2S were lower at the O2 injection spots than the non-root cells. In panel c1, the O2 injection spots are outlined in white. Some of the O2 injection spots are unrecognizable by color on the heatmap because they are masked by an extreme value, which is the spot with an O2 concentration of 100% saturation

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Homogeneous ROL had small impacts on CH4 concentration but large impacts on the H2S and SO42− porewater concentrations (Fig. 4). ROL_Hom predicted the same CH4 concentration as noROL (Fig. 4a, b), which contradicts our hypothesis that simulated ROL will reduce porewater CH4 concentration. Due to the enhanced H2S oxidation, ROL_Hom predicted 5 mmol L−1 lower H2S and 5 mmol L−1 higher SO42− concentrations than noROL (Fig. 4a, b). Heterogenous ROL resulted in heterogeneous distribution of all redox sensitive species at the rooting zone. Among them, the distribution patterns of CH4 and H2S were opposite to that of O2 due to aerobic oxidation occurring in the root cells, i.e., lower CH4 and H2S at the root cells than non-root cells and noROL, consistent with our hypothesis that ROL simulation will reduce CH4 concentration at the root tips (Fig. 4c).

Mean concentration profiles

The mean concentration profiles differed between the three ROL simulations at the rooting zone (7.5–15 cm deep). Mean O2 concentration increased from zero in noROL to 0.01% saturation in ROL_Hom and 2% saturation in ROL_Het (Fig. 5a). Mean CH4 concentration was 0.70 mmol L−1 in ROL_Hom, the same as noROL, and it was 0.83 mmol L−1 in ROL_Het, i.e., 18% higher than noROL (Fig. 5b). Simulated ROL had pronounced impacts on the mean H2S concentration, which was 84% lower in ROL_Hom and 73% lower in ROL_Het compared to the noROL simulation (Fig. 5e).

Fig. 5
figure 5

Mean porewater concentration profiles of the 100 columns of the simulation domain from the three ROL simulations. Note that the concentration profiles of O2 (panel a) and CH4 (panel b) of ROL_Hom and noROL overlap with each other. Differences between the three ROL modes were observed at the rooting zone, 7.5–15 cm deep. ROL_Hom had very little impact on O2 (panel a), CH4 (panel b), and DOC concentrations (panel c). ROL_Het resulted in higher O2 (panel a), CH4 (panel b), and lower DOC averaged concentrations (panel c) than noROL at the rooting zone. Both ROL_Hom and ROL_Het predicted much higher SO42− (panel d) and much lower H2S (panel e) averaged concentrations at the rooting zone when compared to noROL. The horizontal axis of panel a was plotted in log scale to visualize the changes in O2 saturation.

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The impact of spatial heterogeneity on CH4 concentration partly contradicts our Hypothesis 2 that simulated heterogenous ROL will decrease CH4 concentration and CH4 emissions compared to the homogenous ROL simulation. ROL_Het predicted 18% higher mean CH4 concentration than ROL_Hom (Fig. 5b). For other species, ROL_Het predicted higher mean O2 concentration (2% saturation, ROL_Het vs. 0.01% saturation, ROL_Hom), 63% higher mean H2S concentration, and 9% lower mean SO42− concentration than ROL_Hom (Fig. 5c–e).

Methane fluxes

ROL_Het predicted lower plant-mediated fluxes and total fluxes of CH4 than noROL while ROL_Hom predicted very close fluxes compared to noROL (Fig. 6), partially consistent with Hypothesis 1 that simulated ROL will reduce CH4 fluxes. The plant-mediated CH4 flux was 5.65 mmol m−2 d−1 in noROL, 5.63 mmol m−2 d−1 in ROL_Hom and 4.74 mmol m−2 d−1 in ROL_Het. The lower plant-mediated CH4 flux in ROL_Het reflects the enhanced CH4 oxidation at the root cells (Fig. 47c), which reduced CH4 availability at the root cells that drive the plant-mediated transport flux. Because the other two flux components, surface diffusion and ebullition, were very close between ROL_Het and noROL, the lower plant-mediated flux drove a 5% lower total CH4 flux in ROL_Het (16.4 mmol m−2 d−1) than noROL (17.2 mmol m−2 d−1) (Fig. 6). The impact of spatial heterogeneity on the CH4 flux was reflected by a 16% lower plant-mediated flux and a 5% lower total flux in ROL_Het than ROL_Hom (Fig. 6).

Fig. 6
figure 6

Predicted individual flux components and the total fluxes of CH4 from the three ROL simulations. ROL_Hom predicted CH4 fluxes very close to noROL (plant-mediated flux slightly lower than noROL). ROL_Het predicted a lower plant-mediated flux and total flux than noROL. Note that plant-mediated transport of CH4 was implemented in the noROL mode despite no O2 input (see Sects. Different modes of ROL simulation and Simulation and calculation of CH4 fluxes)

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Across all ROL simulations, ebullition contributed the most to the total flux (54–58%), while plant-mediated transport (29–33%) and diffusion (13%) contributed less. For vegetated wetlands, our values for plant-mediated transport are on the low end of the observed range of fluxes (reviewed in Vroom et al. 2022). We interpret this as a likely overestimation of ebullition in our parametrization for the following reasons: (a) our reaction network does not include anaerobic CH4 oxidation which can lower CH4 concentrations below the rooting zone and (b) our parametrization instantaneously removes methane as ebullition, once it is supersaturated in porewater. This does not take into account the physical properties of peat controlling the gas phase in peaty soils (Terry et al. 2016; Wright et al. 2018).

Sensitivity analysis

We tested how the differences in model output between the heterogeneous and homogeneous simulation would change with different values of the model input. For conciseness, “difference” in this section refers to the percentage difference between ROL_Hom and ROL_Het in the mean porewater concentration of the cell arrays of the rooting zone at ca. 10 cm depth or the difference in the total CH4 flux integrated over the simulation domain. Percentage differences between ROL_Het and ROL_Hom was calculated following Eq. S2. A positive percentage difference means that the result from ROL_Het was higher than ROL_Hom.

Using a higher total O2 injection rate in our model, the differences in O2 and H2S concentration greatly enlarged but differences in other output variables only slightly enlarged or shrank (Table 4). When O2 injection rate was increased from 72 mmol m−2 d−1 to 100 mmol m−2 d−1, mean O2 concentration in ROL_Het increased from 2% saturation to 126% saturation while remained at 0% in ROL_Hom. The difference in H2S concentration increased from 63% to 5,274% and the total CH4 flux increased 5–6%. However, the difference in CH4 porewater decreased from 19 to 16%. When using a smaller O2 injection rate, 60 mmol m−2 d−1, the difference in H2S concentration shrank to 8% (Table 4).

Using a higher number of root cells in our model while keeping the injection rate constant, i.e., a more homogeneous distribution of O2 input, the differences in all output variables between ROL_Het and ROL_Hom became smaller (Table 4). The number of root cells had the greatest impact on O2 concentration. By increasing the number of root cells from 15 to 70, the difference in O2 concentration shrank (O2 in ROL_Het decreased from 2.19% sat. to 0.01% sat. while it was always 0.01% in ROL_Hom), and the difference in the total CH4 flux shrank from 5 to 0% (Table 4).

Using higher \({K}_{{O}_{2}}\) values for aerobic oxidation reactions in our model, the differences in O2 concentration between ROL_Het and ROL_Hom became smaller. By increasing the \({K}_{{O}_{2}}\) from 3% saturation to 40% saturation, the difference in O2 concentration shrank (O2 in ROL_Het decreased from 2.19% sat. to 1.13% sat. while it was always 0.01% sat. in ROL_Hom) (Table 4). However, the differences in other porewater species and the total CH4 flux did not change with the different \({K}_{{O}_{2}}\) (Table 4).

When sulfur cycling was excluded, O2 saturation in the rooting zone for ROL_Het (92%) was significantly higher than ROL_Hom (2%). CH4 concentrations at the rooting zone were higher (18%) in ROL_Het than in ROL_Hom, as they were in our other runs for the sensitivity analysis. Similarly, the overall impact on total CH4 flux remained 5%. The largest impact of ROL parametrization with and without sulfur cycling was apparent in the DOC concentration profile. DOC concentrations at all depths in ROL_Het and ROL_Hom were higher by nearly a factor of two in the model run without S compared to the one with S cycling (Fig. S3). In the rooting zone, mean DOC concentrations were 17% less in ROL_Het than ROL_Hom with S cycling, while without S cycling they were 4% larger (Table 4).

Table 4 Percentage differences in the mean porewater concentration in the rooting zone and in the overall CH4 flux between ROL_Het and ROL_Hom when different values of the model input were used
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Discussion

Implications of ROL parameterization

Our results show that the parametrization of ROL influences simulation of methane and sulfur cycling in coastal wetlands, but that the difference between ROL_Hom and ROL_Het on the domain scale (i.e., on the domain-integrated CH4 flux) are less than on the root scale (i.e., on the porewater concentration at the individual cells).

The ROL simulations (ROL_Hom and ROL_Het) predicted the same or slightly higher mean CH4 concentration at the rooting zone and lower CH4 fluxes compared to noROL, which partly contradicts our hypothesis that simulated ROL will reduce porewater CH4 at the rooting zone and CH4 flux. This result indicates that in ROL_Hom, the injected O2 is not sufficient to change the CH4 concentration compared to noROL. In ROL_Het, the O2 was concentrated at the root cells and thus the rooting zone was dominated by the non-root cells with no O2 and no CH4 oxidation, which resulted in higher CH4 concentration averaged across the rooting zone in ROL_Het than noROL. It should also be noted that the absence of anaerobic oxidation of methane may have influenced our predictions of methane flux. Since there are significant differences in sulfate/sulfide concentrations between scenarios, the interactions between the sulfur and methane cycles could exaggerate the trends observed in these simulations. While oxygen may directly oxidize methane, if sulfide oxidizers are faster at utilizing the oxygen than methane oxidizers, the indirect effect of increased sulfate may be a key factor in predicting methane flux. Although the inclusion of anaerobic oxidation of methane is not within the purview of this study which uses a simplified reaction network, it should be included in future studies.

The ROL_Het simulation predicted higher mean CH4 and H2S concentrations at the rooting zone and lower CH4 flux compared to ROL_Hom, which partly contradicts our hypothesis that simulated heterogeneous ROL will decrease CH4 and H2S concentrations and CH4 emissions compared to homogeneous simulation. This increased CH4 and H2S concentrations and CH4 emissions because in ROL_Het, although heterogenous O2 injection created hotspots of aerobic oxidation, the rooting zone was dominated by the non-root cells with no O2 and no H2S or CH4 oxidation, whereas in ROL_Hom, H2S and CH4 oxidation occurred in all cells of the rooting zone. For the CH4 fluxes, in ROL_Het, the plant-mediated transport was implemented heterogeneously, thus CH4 was removed only from the root cells, where CH4 concentration was low due to ROL and CH4 oxidation at the root cells, and the non-root cells had high CH4 concentrations but did not contribute to the CH4 flux in the ROL_Het mode. Therefore, the low CH4 concentration at the root cells drove a low CH4 plant-mediated flux in ROL_Het. This shows that heterogeneous ROL affects the spatial distribution of CH4 at the rooting zone, which further influences the plant-mediated CH4 flux and total flux.

In the simulations including sulfur cycling, sulfate reduction competed for the DOC substrate with methanogenesis, thus causing a lower CH4 production and a lower ebullition flux, compared to no-sulfur cycling simulations. Also, sulfide oxidation can intensively compete for O2 and thereby limit the aerobic oxidation of CH4, because sulfide oxidation can have a rate constant, \({\nu }_{max}\), two to three orders higher than CH4 oxidation (Boudreau et al. 1998; Furukawa et al. 2004). Thus, our study suggests that the rapid uptake of O2 by sulfide oxidation could mitigate the impact of ROL on CH4 concentrations and fluxes in wetlands with high sulfide concentrations by reducing the amount of O2 available for CH4 oxidation. Simulated ROL caused a 63% decrease in H2S concentration (5.2 mM, noROL vs. 0.8 mM, ROL_Hom) at the rooting zone via the rapid sulfide oxidation. H2S is a phytotoxin that can cause adverse effects on plant growth (Lamers et al. 2013; Martin and Maricle 2015), but our simulation showed that ROL could have drawn down the H2S concentration from above to below the toxicity threshold of many plant species in salt marshes (Lamers et al. 2013), e.g., 0.92 mM for Typha domingensis (Li et al. 2009). This indicates that including ROL simulation into ecosystem modeling as a control on H2S concentration could benefit the modeling of primary productivity in coastal wetlands and could potentially become more important for coastal marshes with increasing salinization driven by sea level rise.

Our results predicted higher ebullitive flux than plant-mediated flux of CH4 for coastal wetlands, which differs from observations of lower ebullitive flux than plant-mediated flux typically in rice paddies (Holzapfel-Pschorn et al. 1986; Butterbach-Bahl et al. 1997). This could be caused by the much higher organic carbon content in the coastal wetland (Giblin and Hopkinson 2023), which led to the much higher methanogenesis rate in our modelling for coastal wetland sediments compared to paddy soils. A higher methanogenesis rate at the anoxic zone would cause more CH4 production, and thus a higher ebullitive flux that can exceed the plant-mediated flux. In addition, in our simulation domain, the anoxic zone (15–70 cm deep), where methanogenesis solely drove the ebullitive flux without methane oxidation, was much bigger than the rooting zone (7.5–15 cm deep) where plant-mediated flux occurred, supplying the high ebullition flux in our modeled results. Here we suggest that model development for simulation of ROL and subsurface biogeochemistry will benefit from accurately locating the rooting zone and anoxic zone of wetland soil profiles through field observations.

Magnitudes of impacts of the simulated ROL and heterogeneity

Sensitivity analysis showed that with a higher O2 injection rate, a more heterogeneous root distribution, or a lower \({K}_{{o}_{2}}\), the differences in the modeled O2 and H2S concentrations between ROL_Het and ROL_Hom enlarged, but the differences in other constituents’ concentrations and in CH4 fluxes were not sensitive to changes in those input variables. Thus, incorporating the ROL simulation in a heterogeneous manner into ecosystem modeling becomes more important to predict O2 and H2S porewater concentrations under those conditions. Previous work has reported seasonal, diurnal, and inter-specific variations in O2 injection rate via ROL (Caffrey and Kemp 1991; Frederiksen and Glud 2006; Matsui Inoue and Tsuchiya 2008). Higher O2 injection rates were reported during growing seasons (Caffrey and Kemp 1991; Frederiksen and Glud 2006), so the incorporation of heterogeneous ROL should be prioritized for those time periods. Further studies are needed for determining species-specific ROL flux of coastal wetlands plants and the Monod half-saturation constants for aerobic oxidation.

We consistently found from the sensitivity analysis that the largest differences between ROL_Het and ROL_Hom were in O2 (mean O2 concentration 0.1-100% saturation in ROL_Het vs. 0.01% saturation in ROL_Hom) and H2S concentrations (1%–5,274% difference), followed by CH4 concentration showing a relatively smaller difference (2–19% difference), which can be attributed to the much faster rate of H2S oxidation than CH4 oxidation. It suggests that incorporating heterogeneous ROL simulation can particularly improve predictions of O2 availability and concentrations of the porewater constituents that can be rapidly oxidized, e.g., H2S.

We found relatively large impacts of heterogeneous ROL on the modeled O2 and H2S concentrations at the root scale, but the impact of spatial heterogeneity of ROL on the total CH4 flux at the domain scale was small (5% difference between ROL_Het and ROL_Hom). That was because in our model neither ebullition nor surface diffusion was affected by the heterogeneity of plant-mediated O2 input and CH4 transport. Ebullition only occurred below the rooting zone where CH4 concentration can exceed the ebullition threshold (1.4 mM). Ebullition was influenced by sulfate reduction, which competed for DOC substrate with methanogenesis, reducing methane production and ebullition flux. Our results are consistent with early work of modeling CH4 fluxes under the influence of plant-mediated gas transport from a single-root scale to a plot scale (Segers and Leffelaar 2001a, b; Segers et al. 2001). They implemented different strategies of simulations and found severe impacts of heterogeneous plant-mediated gas transport on biogeochemical processes (> 80% difference in porewater CH4 concentration) at the root scale but a small effect on the integrated CH4 flux (< 10% difference between homogeneous and heterogeneous simulations).

The absolute difference in the total CH4 flux, 0.9 mmol m−2 d−1, or 5 g CH4 m−2 yr−1, between ROL_Het and ROL_Hom is comparable to the uncertainty (one standard deviation) reported for CH4 emissions measurements of mesohaline marshes (± 11 g CH4 m−2 yr−1) and polyhaline marshes (± 2 g CH4 m−2 yr−1) (Poffenbarger et al. 2011). It is also within the error of the modeled relative to the measured CH4 fluxes in salt marshes (e.g., ± 0–70 g CH4 m−2 yr−1, Shu et al. 2020; Yuan et al. 2021). Therefore, the impact of heterogeneous ROL on model predictions of CH4 fluxes is small and within measurement error, but it could be more important under conditions of higher ROL flux and more heterogeneous root distribution, requiring further information of these parameters from field measurements.

Model limitations

Our model was designed to test the impacts of ROL in a short-term simulation. We did not include environmental components such as tidal dynamics, diel and seasonal variations of temperature, plant productivity, or nutrient subsidies because including these temporal dynamics would complicate the interpretation of the impacts of ROL. It has been suggested that the heterogeneity caused by ROL within the rooting zone might be less important to soil biogeochemistry than the vertical heterogeneity between different soil layers caused by water table fluctuations (Segers and Leffelaar 2001b). This also has important implications for scaling since incorporating this level of heterogeneity at scale could be computationally expensive. In this system, which has a very dense root mat, representation of a horizontally homogeneous plant mediated transport layer may be sufficient to describe the influence of ROL. However, this should be investigated in terms of temporal heterogeneity that was not included in our relatively short simulation timeframes. Diel variation in ROL flux, can cause diel variations in oxidation rates of organic substrate and methane oxidation and thus methane emissions (Ding et al. 2004; O’Meara et al. 2024). In addition, tidal dynamics can drive temporal variations in porewater salinity and H2S concentration, affecting plant growth including the developments of aerenchyma (Matsui Inoue and Tsuchiya 2008; Munns and Tester 2008; Lamers et al. 2013) and thus ROL fluxes. Further studies are therefore needed to investigate how ROL fluxes are controlled by temporal fluctuations including diel cycles such as tides or stomatal opening/closure to improve representation of ROL in subsurface biogeochemical models.

Our model used a simplified reaction network while omitting anaerobic CH4 oxidation, due to the lack of measured reaction rate parameters from coastal wetland ecosystems. As shown above, ROL significantly increased sulfide oxidation at the rooting zone. Sulfide oxidation can suppress aerobic oxidation of CH4, but the product of sulfide oxidation, sulfate, can drive anaerobic oxidation of CH4 (Smemo and Yavitt 2011; Blazewicz et al. 2012; Cui et al. 2015). This can further remove CH4 and counteract the sulfide suppression of CH4 aerobic oxidation, which means that our model might have underestimated the impacts of ROL on CH4 cycling. We therefore need more work to measure reaction rate parameters for understanding of how ROL affects methane cycling in sulfur-rich environments like coastal wetlands.

Our model did not simulate root exudates containing labile organic substrates which can enhance methane production in the rhizosphere as well as surface methane emissions. Previous studies have indicated the opposing effects of root exudates and ROL, as ROL can enhance methane oxidation (Gerard and Chanton 1993; Sutton-Grier and Megonigal 2011; Noyce et al. 2023). Therefore, the impacts of ROL on CH4 cycling (porewater concentrations and emissions) can be partially offset by the impacts of root exudates. Furthermore, cable bacteria have been shown to play a significant role in reducing soil CH4 emissions by enhancing the competition between sulfate reduction and methanogenesis, via electrogenic sulfide oxidation that increases the sulfate level (Martin et al. 2019; Scholz et al. 2020). Organic carbon oxidation in our model is partially controlled by the O2 concentration, but a more detailed mechanism could include anoxic conditions preventing phenol oxidase from degrading phenolic compounds that inhibit organic carbon decomposition (Freeman et al. 2001). Incorporating these factors into future models would require parameterization informed by measurements such as the root exudation rates, substrate degradation rates, bacteria growth rates, and O2 controls over specific enzymes.

Modelling implications and recommendations

Since efforts are already under way to couple PFLOTRAN to land surface models (Sulman et al. 2024), our findings have implications for parametrizing soil-plant interaction and CH4 fluxes in wetlands. It is important to state that we parametrized our model for a well – studied wetland plant, T. angustifolia, for which ROL rates have been published (Matsui Inoue and Tsuchiya 2008). In terms of rooting depth, this plant is known to have relatively shallow roots (Bansal et al. 2019). In comparison, O’Meara et al. (2024) parametrized PFLOTRAN for Schoenoplectus americanus which has a greater rooting depth (0 to 0.6 m) than T. angustifolia (0–0.12 m). To take this into account, O’Meara et al. (2024) simulated ROL at three different depths instead of one layer as in our study, using an injection rate which is larger the one we use (0.08 L/s of O2 vs. 0.016 L/d in our study). While the authors did not measure ROL, the chosen rate – together with a complex redox reaction network—improves the agreement between observations and predictions of redox sensitive constituents. Interestingly, O’Meara et al. (2024) demonstrate an increase of relevance of plant-mediated transport along the soil concentration profiles, likely a function of different rooting depths and ROL injection at different depths as opposed to our more localized impact. This indicates the importance of considering species-specific parametrizations (Määttä and Malhotra 2024) and the challenges associated with characterizing plant functional types (PFTs) instead of species (LaFond-Hudson and Sulman 2023). Based on our findings, we recommend testing the impact of different plant structures and developing simplified parametrizations in an intermediate model like PFLOTRAN (O’Meara et al. 2024) before deploying the latter in the land surface models, similar to the step-wise scaling approach described by Segers and Leffelaar (2001a).

It should be noted, that other important aspects for parametrizing plant functional types for coastal wetlands is the sulfide tolerance of the vegetation and its tolerance of salinity stress, which impacts species distribution and productivity (LaFond-Hudson and Sulman 2023). The ability of wetland plants to generate an oxygenated rooting zone strongly controls their sensitivity to phytotoxin compounds (Lamers et al. 2013), which is an additional reason beyond flood tolerance to consider in wetland plant PFTs. PFLOTRAN is not designed to simulate vegetation processes, but once coupled to a dynamic land surface model, incorporating gas transport and ROL can be targeted. Our target species, T. angustifolia, grows in freshwater or brackish systems and its productivity and root-shoot ratio displayed great variability as a function of salinity (Whigham et al. 1989) and would be a good target for parametrizing a brackish plant functional type.

Conclusions

Existing biogeochemical models of wetland carbon cycling do not include fine-scale spatial heterogeneity of oxygen concentrations and other key biogeochemical drivers of coastal wetland ecosystem function. The goal of our study was to determine whether this omission can drive significant bias in understanding subsurface biogeochemical cycling. To do so, we parametrized a simplified reaction network and tested different parametrizations of root oxygen release and its impact on porewater constituents in the rooting zone and column-integrated methane fluxes. Our results show that not only the parametrization of ROL but also that of plant-mediated transport influences simulation of methane cycling in coastal wetlands, and that the impact varies on root and domain scales. Simulated homogeneous ROL predicted CH4 concentration same as the no ROL simulation and the simulated heterogenous ROL reduced CH4 concentration at the root cells compared to the no ROL simulation, which partially fulfilled our hypothesis 1 (“simulated ROL will reduce CH4 concentration at the rooting zone”). Heterogeneous ROL simulation predicted 18% higher mean CH4 concentration at the rooting zone and 5% lower total CH4 flux, compared to the homogeneous ROL simulation, which partially fulfilled our hypothesis 2 (“simulated heterogeneous ROL will decrease CH4 and H2S concentrations and CH4 emissions compared to homogeneous ROL simulation”). Heterogeneous ROL had bigger impacts on porewater concentrations at the root scale but weak impacts on CH4 fluxes at the domain scale. The heterogeneous ROL simulation caused lower CH4 flux by reducing the CH4 concentration at the root cells for the heterogeneous plant-mediated transport. These results are robust, because we did not observe changes in mean CH4 concentrations or fluxes in our sensitivity analysis, including when we change the availability of alternative electron acceptors, i.e. sulfur compounds. Only when we increase the number of roots do we see the two simulations getting closer in agreement, which is due to the fact that we restrict our simulations to injecting the same amount of oxygen. Despite the small impact of ROL on methane fluxes, ROL can induce large removal of porewater sulfide, an effect of similar magnitudes observed both in the homogeneous and heterogeneous simulations. Thus, incorporating ROL simulation into ecosystem modeling could benefit predictions of plant productivity which is adversely affected by porewater H2S.